How do you know if $f(x) = x^3 + x sin^2 x$ is an even or odd function?

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Answer 1 · 2015-11-28T09:43:30

Use $sin(-x) = -sin(x)$ and find $f(-x) = -f(x)$ so $f$ is odd.

$f(-x) = (-x)^3+(-x)(sin(-x))^2$

$=-x^3-x(-sin(x))^2$

$=-x^3-x (sin(x))^2$

$=-(x^3+x (sin(x))^2)$

$=-f(x)$

How do you know if f(x) = x^3 + x sin^2 xf(x) = x^3 + x sin^2 x is an even or odd function?